Bell inequalities for three particles

Abstract

We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. The tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities of three qubits reduced from those of three qudits are also studied.

8 pages, 3 figures. Accepted for publication in Phys. Rev. A

References in corpus (11)

• Device-independent security of quantum cryptography against collective attacks
• Bell inequalities for arbitrarily high dimensional systems
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Violations of local realism by two entangled quNits are stronger than for two qubits
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Bell's theorem for general N-qubit states
• Spectral decomposition of Bell's operators for qubits
• Do all pure entangled states violate Bell's inequalities for correlation functions?
• Gisin's Theorem for Three Qubits
• Greenberger-Horne-Zeilinger paradoxes for many qudits
• Greenberger-Horne-Zeilinger paradoxes for N quNits

Cited by in corpus (8)

• Bell nonlocality
• Reexamination of a multisetting Bell inequality for qudits
• Complete proof of Gisin's theorem for three qubits
• Multipartite Bell-type Inequality by Generalizing Wigner's Argument
• Bell inequality for qubits based on the Cauchy-Schwarz inequality
• Chain of Hardy-type local reality constraints for $n$ qubits
• Investigating nonclassicality of many qutrits by symmetric two-qubit operators
• Degree of Fuzziness in Coarsened Measurement References